Abstract
Discovery of twodimensional (2D) topological insulator such as groupV films initiates challenges in exploring exotic quantum states in low dimensions. Here, we perform firstprinciples calculations to study the geometric and electronic properties in 2D arsenene monolayer with hydrogenation (HAsH). We predict a new σtype Dirac cone related to the p_{x,y} orbitals of As atoms in HAsH, dependent on inplane tensile strain. Noticeably, the spinorbit coupling (SOC) opens a quantum spin Hall (QSH) gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edges, and its QSH phase is confirmed with topological invariant Z_{2} = 1. We also propose a 2D quantum well (QW) encapsulating HAsH with the hBN sheet on each side, which harbors a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.
Introduction
Twodimensional (2D) topological insulators (TIs), known as quantum spin Hall (QSH) insulators, have attracted significant researches interest in condensed matter physics and materials science. The unique characteristic of 2D TI is generating a gapless edge state inside the band insulating gap, in which the edge state is topologically protected by timereversal symmetry (TRS)^{1,2} and more robust against backscattering than the 3D TI, making 2D TIs better suited for coherent spin transport related applications. The prototypical concept of QSH insulator is first proposed by Kane and Mele in graphene^{3,4}, in which the spinorbit coupling (SOC) opens a band gap at the Dirac point. However, the associated gap due to rather weak secondorder effective SOC is too small (~10^{–3 }meV), which makes the QSH state in graphene only appear at an unrealistically low temperature. Quantized conductance through QSH edge states have been experimentally demonstrated in HgTe/CdTe^{5,6} and InAs/GaSb^{7,8} quantumwells (QWs), showing an interesting in further experimental studies and possible applications.
Currently, there is a great interest in searching for new QSH insulators in 2D materials with controllable quantum phase transitions and tunable electronic and spin properties. Remarkably, the orbital filtering effects (OFE) in engineering the band feature has been received intense attentions in designing QSH insulators. For instance, stanene^{9} has a small band gap of 0.1 eV where the p_{z} orbital dominates the effective lowenergy band structure. Through hydrogenation, the SOC can be confined both on the p_{x} and p_{y} orbitals of stanene, enhancing its band gap to 0.3 eV. In fact, the band gap enhancement in QSH phase can also be realized by decorating organic molecule ethynyl on stanene film^{10}. The strong SOC can be sufficed by bismuth element, which drives QSH and QAH states^{11}. More recently, an approach to design a largegap QSH state on a semiconductor surface by a substrate orbital selection process is also proposed^{12}. These demonstrate that OFE is an effective way to enhance QSH effect in 2D materials with s and p orbitals dominating the conduction and valence bands.
GroupV honeycomb structures have recently attracted interests as novel 2D materials with intriguing electronic properties. Interestingly, the monolayer form of black phosphorous, phosphorene (αP), has been reported experimentally to have a direct band gap and high carrier mobility, which can be exploited in the electronics^{13,14}. The Bi or Sb ultrathin films^{15,16,17,18}, another 2D groupV films with the strongest SOC, have been proposed to harbor largegap QSH phases, ample to applications at room temperature. More recently, arsenene in α and β phases has been proposed to be energetically stable^{19,20,21,22}. These materials with high mechanical stretchability, which can reversibly withstand extreme mechanical deformation, are useful to stretchable display devices, broadband photonic tuning and aberrationfree optical imaging^{19,20,21}. More importantly, we find the pristine arsenene can be a QSH insulator, but its band gap is relative small, unfavorable to possible room temperature applications^{22}. However, the band topology of hydrogenated arsenene (HAsH) have not been reported up to date. It is thus reasonable to ask whether or not HAsH becomes a nontrivial QSH insulator, which maybe largely widens its application in spintronics.
In this work, based on firstprinciples calculations, we predict a σtype Dirac cone at the K point in HAsH. The key is the OFE from decorated hydrogen atoms, in which the outofplane p_{z} is filtered from p orbitals, forming sp^{2} hybridization, in analogy to planar graphene. A QSH phase with a bandgap as large as 193 meV at the Fermi level is obtained, available to practical application at room temperature. A single pair of topologically protected helical edges is established, and its QSH phase is confirmed with Z_{2} = 1. We also propose a QW encapsulating HAsH between the BN sheet on each side, maintaining a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN substrate. These results provide an ideal platform for development of highperformance electronic devices in spintronics.
Methods
Firstprinciples calculations based on densityfunctional theory (DFT)^{23} are performed by the Vienna ab initio simulation package^{24}, using the projector augmentedwave potential. The exchangecorrelation functional is treated using the PerdewBurkeErnzerhof (PBE)^{25} generalizedgradient approximation. The energy cutoff of the plane waves is set to 500 eV with the energy precision of 10^{–5 }eV. The Brillouin zone (BZ) is sampled by using a 9 × 9 × 1 Gammacentered Monkhorst–Pack grid, and the vacuum space is set to 30 Å to minimize artificial interactions between neighboring slabs. All structures are fully optimized, including cell parameters and atomic coordinates, until the residual forces are less than 0.01 eV/Å. The SOC is included in the selfconsistent calculations of electronic structure.
Results and Discussion
Bulk As has four allotropes, and the most stable one is gray As^{20}, which is rhombohedral with two atoms per primitive cell. Thus, it can be viewed as a stacking of the bilayers along the [111] direction, as shown in Fig. 1(a). Unlike the planar graphene, the arsenene has a buckled configuration with a buckling distance h = 1.39 Å and bond length d = 2.51 Å (Fig. 1(b)), in consistent with that of Ref. 19 and 20. Figure 1(c) displays the calculated band structures of arsenene, which is indirectgap semiconductor with a gap of 1.64 eV at the Fermi level. In this respect, its valence band maximum (VBM) locates the Γ point, while conduction band minimum (CBM) on MΓ path, in agreement with the previous results^{20}.
Hydrogenation has been proven to be an efficient way in engineering the electronic properties in 2D materials^{10,26,27,28,29,30,31,32}. Thus, we saturate the uncoordinated As atoms with hydrogen atoms alternating on both sides of As sheet, in which d_{1}−d_{4} represents the various bond lengths between As atoms (Fig. 1(d)). In sharp contrast to the graphane and silicane^{33,34}, the structural relaxation make the σbond direction of AsH atoms tiled and finally perpendicular to AsAs bonds, indicating hydrogeninduced arsenic dimerization with respect to tensile strain, as listed in Table 1. Figure 1(e) gives the total energy per unit cell as a function of lattice constant a. Interestingly, it displays two local minima in energy, where refer to the corresponding stable phases as buckled and planar states in order to highlight the size of buckling or interlayer distance in these two distinct states (Table 1).
External strains can drastically change the geometric structures, and thus influence the electronic properties of HAsH correspondingly. As shown in the insert of Fig. 2, when applying the tensile strain, the As–As dimerization occurs clearly, leading to an indirectdirect gap transition. Further increasing to 4.20 Å, the AsAs dimerization is suppressed, along with the arsenene plane becoming flat. In this case, a clear band crossing appears at the K point (Fig. 2(c)), as compared with the original indirectgap semiconductor feature. If the lattice constant reaches 4.64 Å, it becomes completely flat with As–As bonds being equivalent, due to the complete dimerization breaking (Fig. 2(d)). The two energy bands crosses linearly at the K (and K′ = −K) point, suggesting the existence of Diraccone feature without SOC. Thus it can be considered as a gapless semiconductor, or alternatively, as a semimetal with zero density of states at the Fermi level. Further increasing the lattice constant, the Diraccone preserves with the crossing at the Γ point shifting toward higher energy, which can be attributed to the simultaneous release of outofplane buckling in arsenene. For instance, if the lattice parameter increases as much as 28%, i.e., from a = 3.62 Å to a = 4.64 Å, the As–As bonds simply elongate from 2.48 Å to 2.68 Å, only corresponding to a stretch of 8%. As expected, it is geometric transition from buckling to planar one that plays a key role in the presence of the Dirac cone.
To prove the dynamic stability of this structure (a = 4.64 Å), we present the calculated phonon spectrum in Fig. 3(a). All phonon branches are positive, which indicates that this structure is kinetically stable. Moreover, Fig. 3(b) shows 3D band structure around the Dirac point at a = 4.64 Å. we can see two Dirac cones located at the K and K′ = −K points, similar valley symmetry as in graphene^{3,4}. However, the energy spectrum here is no longer electronhole symmetric, thus neither the scattering mechanism nor transport properties will be identical for the electron and hole doping cases. The linear dispersion holds up to 2.0 eV for holes, while the massless electrons acquire mass rapidly away from the K point, demonstrating that it is more promising for making unipolar field effect devices than for making ambipolar ones with graphene.
Now, we highlight the importance of the OFE^{9,10,11,12} in determining the origin of Dirac cone at a = 4.64 Å. In the absence of hydrogen atoms (Fig. 4(a)), one can see two Dirac cones located at the K point. By projecting the component of bands, the upper Dirac cone (green circles) originates from the p_{x,y} orbitals, whereas the lower one (blue circles) originates from p_{z} orbital. Through fullyhydrogenation, the Asp_{z} orbital bond to Hs orbital is filtered, making the low Dirac cone disappear (Fig. 4(b)). Thus, the remaining Dirac cone mainly comes from Asp_{x,y} orbitals rather than from p_{z} orbital, as illustrated by the size of the circles near the Fermi energy. In this case, the p_{x,y} orbitals form σ bonds between AsAs atoms, demonstrating an inplane Dirac cone feature. Figure 4(c) further illustrates the schematic plot of energy level dispersion. As expected, the chemical bonding of AsAs atoms makes the s and p_{x,y} orbitals forming the bonding and antibonding states, in the energy consequence of σ < π < π* < σ*, The planar honeycomb geometry separates inplane (p_{x,y}) and outplane (p_{z}) orbitals, forming their own Dirac cones with σ and π characters, respectively (Fig. 4(a)). The hybridization between the π orbitals and induced H1s orbital suppresses the πtype Dirac cone, leaving the σtype Dirac cone intact. In addition, the Fermi level is raised by introduced hydrogen atoms, and thus forming the semimetallic states.
The As atom has an intrinsically larger SOC than a carbon atom, which may lead to many intriguing quantum properties in arsenene, such as the QSH effect^{3,4,35}, in addition to its massless Dirac fermion as in graphene. To confirm this, we focus on the effect of SOC on band structures at 4.64 Å, as displayed in Fig. 5(a). One can see that the degeneracy at the Dirac points is lifted. The valence bands are downshifted whereas the conduction bands are upshifted, forming a large band gap of 193 meV by SOC, as illustrated in Fig. 4(c). As observed in previously reported 2D TIs like phosphorene^{36}, ZrTe_{5}, HfTe_{5}^{37}, and GaSe^{38}, the SOCinduced bandgap opening at the Fermi level is a strong indication of the existence of topologically nontrivial phases. We have carried out test calculations based on the hybrid functional HSE06 to assess the robustness of our results. As shown in Fig. 5(b), the band gap around Dirac point is increased to 339 meV, but the band character is not changed, which is agreement with our PBE results.
To identify the nontrivial band topology in 2D HAsH, we calculate the topologically invariant Z_{2} number (γ) following the approach proposed by Fu and Kane^{39}, due to the presence of inversion symmetry. Here, the invariants v can be derived from the parities of wave function at the four timereversalinvariant momenta (TRIM) points K_{i}, namely one Γ point and three M points in the Brillouin zone, as illustrated in the insert of Fig. 5(a). The topological index ν are established by
where δ is the product of parity eigenvalues at the TRIM points, ξ = ±1 are the parity eigenvalues and N is the number of the occupied bands. According to the Z_{2} classification, ν = 1 characterizes a QSH insulator, whereas ν = 0 represents a trivial band topology. As expected, in the equilibrium state, the products of the parity eigenvalues at these three symmetry points: M(0.0, 0.5), M(0.5, 0.5) and M(0.5, 0.0) are both −1, while at Γ(0.0, 0.0) and displays +1, yielding a nontrivial topological invariant Z_{2} = 1.
The SOC induced band gap opening near the Fermi level indicates possible existence of 2D TI state that are helical with the spinmomentum locked by TRS. To check this, we calculated the topological edge states of HAsH by the Wannier90 package^{40}. We construct the maximally localized Wannier functions (MLWFs) and fit a tightbinding Hamiltonian with these functions. Then, the edge Green’s function^{41} of a semiinfinite HAsH is constructed and the local density of state (LDOS) is calculated, as shown in Fig. 5(b). Clearly, all the edge bands are seen to link the conduction and valence bands and span the 2D band energy gap, yielding a 1D gapless edge states. Besides, the counterpropagating edge states exhibit opposite spin polarizations, in accordance with the spinmomentum locking of 1D helical electrons. All the above results consistently indicate that hydrogenated arsenene is an ideal 2D TI.
The substrate materials are inevitable in device application, thus the freestanding HAsH monolayer should eventually be deposited or grown on a substrate. As a 2D largegap insulator with a high dielectric constant, the hBN sheet has been successfully used as the substrate to grow graphene or assemble 2D stacked nanodevices^{42,43}. Considering that the HAsH surface is chemically active, we adopt the encapsulation technology, which has been used in FlipChip^{44}, to encapsulate HAsH monolayer forming a hybrid QW from the degradation effect by the environmental gases, which, if not prevented, would destroy the QSH states. Figure 6(a) show the QW structure of HAsH monolayer sandwiched on BN sheet, where the lattice mismatch is only about 6.3%. After full relaxation with the van der Waals (vdW) forces^{45}, HAsH almost retain the original structure with a distance between the adjacent hBN layers of 2.38 Å. The calculated binding energy is about −0.77 eV per unit cell, showing that they are typical van der Waals interactions. The calculated band structure with SOC is shown in Fig. 6(b). In these weakly coupled QW structure, the HAsH monolayer remains semiconducting, there is essentially no charge transfer between the adjacent layers, and the states around the Fermi level are dominantly contributed by HAsH. If we compare the bands of HAsH with and without the cladding BN sheet, little difference is observed. Evidently, the robustness of QSH effect can be preserved in this QW structure.
Conclusions
In summary, based on firstprinciples calculations, we predict a new σtype Dirac cone related to the p_{x,y} orbitals of As atoms in HAsH, dependent on inplane tensile strain. The key is to separate the inplane p_{x,y} and outofplane p_{z} orbitals via hydrogenation and strain. Noticeably, spinorbit coupling (SOC) can open a nontrivial QSH gap of 193 meV at the Dirac cone. A single pair of topologically protected helical edge states is established for the edge of HAsH, and its QSH states are confirmed with topological invariant Z_{2} = 1. We propose a QW encapsulating HAsH between the hBN sheet on each side, maintaining a nontrivial QSH state with the Dirac cone lying within the band gap of cladding BN sheet. These findings provide a promising innovative platform for QSH device design and fabrication operating at room temperature.
Additional Information
How to cite this article: Wang, Y.P. et al. Controllable band structure and topological phase transition in twodimensional hydrogenated arsenene. Sci. Rep. 6, 20342; doi: 10.1038/srep20342 (2016).
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No.11274143, 61571210, and 11304121), and Research Fund for the Doctoral Program of University of Jinan (Grant No. XBS1433).
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School of Physics and Technology, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China
 Yaping Wang
 , Weixiao Ji
 , Changwen Zhang
 , Ping Li
 , Feng Li
 , Miaojuan Ren
 , XinLian Chen
 , Min Yuan
 & Peiji Wang
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Contributions
Y.P.W. and C.W.Z. conceived the study and wrote the manuscript. W.X.J. and P.L. performed the firstprinciples calculations. F.L. and M.J.R. prepared figures 1–2, 6. X.L.C., M.Y. and P.J. Wang prepared figures 3–5. All authors read and approved the final manuscript.
Competing interests
The authors declare no competing financial interests.
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Correspondence to Changwen Zhang.
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